Method and apparatus for color matching



Feb. 6, 1951 E. l. STEARNS, JR,

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METHOD AND APPARATUS FOR COLOR MATCHING Feb. 6, 1951 Filed Nov. 2, 1945 Feb. 6, 1951 E. sTEARNs, .1R 2,540,797

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METHOD AND APPARATUS FOR COLOR MATCHING 13 ,Sheets-Sheet 6 Filed Nov. 2, 1945 Feb. 6, 1951 E. l. sTEARNs, JR 2,540,797

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ATTORNEY Feb. 6, 1951 E. l. sTEARNs, JR

METHOD AND APPARATUS FOR COLOR MATCHING 13 Sheets-Sheet 8 Filed NOV. 2, 1945 Y m AT1-ORN EY Feb. 6, 1951 E. s. sTEARNs, JRA 2,540,797

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METHOD AND APPARATUS FOR COLOR MATCHING Filed Nov. 2, 1945 Feb. 6, 1951 E. l. STEARNS, JR

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METHOD AND APPARATUS FOR COLOR MATCHING 13 Sheets-Sheet 15 M EL Z R J, Y E fo o w M d v @l i x E fo w 4 l m VN y` @L X j ,A .w w d fo J M J M Xo Yo Z0 J N W K x j f. f m w M E W E a p a A, f C

M i E mi, 3 s M. g k 3 w K w 3 v E I .XX M m r c a Q M a 2J x WQ. F 7. M 2, p E. N M M m w n M# /g b Patented Feb. 6, 1951 METHOD AND APPARATUS FOR COLOR MATCHING Edwin I. Stearns, Jr., Plainfield, N. J., assignor to American Cyanamid Company, New York, N. Y., a corporatonvof Maine Application November 2, 1945, Serial No. 626,310

Claims. i

This invention relates to a method of determining tristimulus values of mixtures of a plurality of colors, and particularly to methods of automatically matching the tristimulus values of dyeings with predetermined dyes. IThe invention includes instruments capable of carrying out the above processes.

The scientific specication of colors is in terms of tristimulus values; that is to say, the amount of each of three theoretical and imaginary colors, or stimuli, X, Y and Z,` which will give the same response to the eye as the actual color. While an innite number of sets of tristimuli are possible, including real as well as imaginary colors, in practice a unique set of imaginary colors is employed. This set is characterized by the fact that every color, even spectral colors, can be represented without using a negative amount of any tristimulus, something which would be impossible with real colors, and, further, one, Y, corresponds to the color sensitivity of the human eye. The tristimuli for different illuminants are somewhat dilierent, and, in general, two sets are in common use. one for daylight and one for tungsten light. These are the only ones used in the vast majority of color matching. The description of the tristimulus notation appears in Chapter 1 of the Handbook of C'olorimetry by Dr. Arthur C. Hardv, 1936 edition. Fig. 9 on page 8 of this book shows the spectrophotometric curves of three tristimuli for daylight illumination. This figure is reproduced in Fig. of the drawings which will be described below.

In the past the problem of determining the tristimulus values of a mixture of a plurality of dyes, and particularly the matching of a dyeing with such dyes, has been a matter of importance to the dyestui industry. It is mathematically feasible to determine tristimulus values of mixtures oi dyes from the reflectance values of the separate dyes by extensive and time consuming mathematical calculations. This method of solution permits the matching of an unknown dyeing with a mixture of predetermined dyestuffs but it involves excessive time. The mathematical operations, even with the aid of new equation technique, are still slow and the operation requires the assumption of starting concentrations or the noiors series of cut and try solutions with various concentrations. It may reduire hours to obtain a satisfactory match by this methed.

The present invention relates to a method of solving the problem and to apparatus for carrying out the method in which the spectral curves of the dyestuiis to be used to match a given dyeing are divided into a series of selected, or preferably weighted, ordinates. The number of wave length ordinates chosen depends on the accuracy desired in the determination of the tristimulus values of a mixture of dyes. The accuracy increases very rapidly with multiplication of ordinates chosen up to an order of magnitude of about 8 to 12 ordinates. When the dye components are sensibly chosen additional ordinates do not add to the accuracy of the result suiciently greatly to warrant the additional complexity which they introduce in the mechanical methods of handling the data according to the present invention. For practical color matching ten or eleven properly selected ordinates give suicient accuracy, and except for special scientific problems larger numbers do not give results which are worth the additional complication.

The present invention gives instantaneous or substantially instantaneous registration of the tristimulus value of a mixture of any concentrations of a plurality of known dyestuiis. When a match is sought by the cut and try method the matching is not automatic. However, the enormous increase in speed of determining each trial mixture cuts the time down to a very small fraction of that now required. Broadly, therefore, the present invention might be considered as including methods and apparatus for giving a substantially instantaneous determination of tristimulus values of any mixture of a plurality of dyes in various concentrations. In a more specific aspect, however, theV invention goes beyond this sub-combination of steps and provides for substantially instantaneous matching of any dyeing, the tristimulus values of which are known. In this more specic aspect the process and apparatus automatically varies the proportions of the dyes in the mixtures until one is reached which matches the unknown dyeing.

The term substantially instantaneous used in both of these modifications requires slight elaboration. In the sub-combination which gives tristimulus values for any mixture the results are obtained in a time interval of the order of magnitude of from a fraction of a second to several seconds. The preferred modiication of the process which provides for automatic matching produces results in a time of the order of magnitude of from a second or two to from one to two minutes. The terms substantially inmeans this particular step in the solution ofy the 7 problem is not considered to form a part of the present invention, although the information obtained thereby, namely, constitutes part of the data used in carrying out the process of the present invention.

The rst step of the process of the present invention involves the transformation of the ordinates selected from the spectrophotometric curve of each of the dyestuis to be used ina mixture, and if desired the substrate such as cloth or other fabric to be dyed, into a physical force which is substantially instantaneously additive. This force must be proportional to the product of dye concentration with the additive function of the dye, which will be referred to as K. K is substantially proportional to where R is percentage reflectance.

The description of the development of the formula for the additive absorption functionK is to be found in the United States patent to Pineo, No. 2,218,357, where it is pointed out that some of the light striking a dyed fabric is reflected from the surface; that is to say, non-selectively as far as color is concerned. The rest of the light penetrates various distances into the'fabric and is selectively absorbed by the dyestuif molecules, which results in color. tion and claims the surface reflectance will be referred to as s, and the light reflected after passing through paths of various lengths in the fabric as 19, the so-called body reflectance. The Pieno patent evelo'ps K in terms of b. For most fabrics, of which Wool istypical, s issmall, though not negligible. While K is substantially proportional to it is not exactly proportional, and the V,relation will vary slightly with different fabrics by the amount of the surface reflectance s.

In the cases of transmission samples, mixtures of fibers and other color applications, there are additive functions K but these functions differ mathematically from K for reflectance given above. Some of these other additiveV functions are described in the American Dyestuff Reporter, volume 33, page 177, and the patent to Pineo, No. 2,176,013, patented October l0, 1939, Thruout, Lthe remainder of this description will deal with K for reflectance as reflectance Samples onstitute the most important eld at the present ime.

The spectrophotometric curve may be used as a physical shape in some of the modifications of the apparatus of the present invention. In other cases it, or spectrophotometer readings, may be used merely to obtain data for the chosen In the specifical the tristimulus values,

ordinates. In the first case it is usually necessary to have a curve which is invariant in shape with concentrations, is proportional to log K, so that linear movement will measure concentration changes on a logarithmic scale. Such a curve can be drawn with a flickering beam spectrophotometer using a varying ratio drive, as describedk in patent to Pineo, No. 2,218,357 referred to above. In general such a curve is a logarithmic function of the extinction coeficiyent of the color for the particular wave length I ordinate. Atain the reflectance data it is desirable to use Where the curve is merely used to oba" curve plotted in terms of the extinction coefficient itself, which is additive for a plurality of dyes, whereas the logarithmic function is not. In the modification in which the spectrophotometric curve is used as a physical entity this may be effected by transforming the chosen ordinates into fixed physical lengths by cutting in rigid material a template having the prole of the curve. This mechanical embodiment of the r'curve may be `used with various modifications of the other steps of the process or elements of theapparatus. It presents advantages in that templates can be readily filed and are cheap to manufacture. It is thus possible to provide a library of templates for all dyes to be used in matching. There is a disadvantage in that one additional step in the process, or correspondingly additional element in the apparatus, is necessary because the lengths of the yordinates represent logarithmic functions and these have to be transformed into their anti-logarithmic equivalents in order to permit their addition, as will be discussed in greater detail below.

When the energy forms for substantially instantaneous addition are to be electrical voltages, the ordinates'may be potentiometers set in accordance with the ordinates of the curve for K. These may be physically moved by templates or lthey may be pre-set manually. In the latter case it is also possible to design the potentiometers in the form of xed tapped resistance which can be provided with plug-in or other quick electrical'connections, and filed, one set for each dye. When the potentiometers are manuallyset or when tapped resistors are used,

4variations in concentrations are usually ex- `pressed'kas changes in the voltage applied tothe potentiometers. other mechanical In the case cf templates -or forms of the spectrophotovmetric curve which can be used to actuate devices `concentration is usually expressed,l on a logarithmic scale, as linear motion of the template.-

Other additive quantities may be used in the place ofvoltages, for example, capacities.` `In one of the steps of the process of the present invention the use of capacities presentsv an advantage that variation can be effected both by shape of the movable condenser plates and by spacings. However, condensers are more delicate and more easily deranged than potentiometers.

The additive quantitiesmay be mechanical in their nature, for example, they may be angular torques produced/by modied forms of chain balances. Other physically additive quantities may be used and the process Aof the present invention is not limited to voltages, capacities, angular torques, etc., described above. The process is also a multi-step process in which it is possible to use more than one type of physical quantity. Thus, for example, an electrical quantity may be used in one or more steps and angular torque in another step, one step may use capacities and another voltages, etc. This great iiexibility of the process is a practical advantage.

While the process is not broadly concerned with the use of any particular means or additive physical quantity, nevertheless the different quantities present advantages and disadvantages, and for most operations there is an advantage in using voltages as the quantities. The circuits and the physical units are more rugged and in some cases more simple, and it is possible in some of the steps of the process to use electronic ampliers to eiect some of the operations. This eliminates the use of many moving parts and adds to the simplicity and reliability of the apparatus for performing the process of the present invention.

The first step of the present invention is to produce an output of the additive quantities as linear or reciprocal functions of K of the dyes and substrates for the chosen ordinates. In the case of processes or apparatus using movable templates this involves logarithmic potentiometers or specially shaped capacitors to transform the logarithmic function of K into a function which is additive. Where the data from a curve is expressed directly in the form of quantities proportional to K or its reciprocal as when potenticmeters, capacities torques are set in accordance with the data from the reectance curve of a particular dye, this change of function is not necessary, but the energy fed to the step must be capable of variation with dye concentration if matching is to be effected automatically.

The additive quantity, such as voltages, capacities, weights, or the like, for each ordinate of each dye and, if desired the substrate, are then added. When these are electrical units they are arranged in circuits so that they add up in series for voltages, parallel for capacities, etc. When the quantities are weights they are attached to the same side of a balance. The addition of the ordinates for the dyes results in the production of a number of quantities equal to the number of ordinates, each quantity representing the sum of the same ordinate for all the dyes. In a typical example where three dyes and one substrate are to be used, the quantity for each ordinate represents the sum of the three dyes and the substrate. If in a typical case where there are eleven ordinates there will be eleven quantities.

The next step is to transform the physical quantities into quantities proportional to the three tristimulus value at each ordinate i. e., R times the tristimulus coeiiicients which will result in a number of quantities three times as great as the number of ordinates. This transformation may be effected in various ways, for example, by comparing the quantity corresponding to the sum for the dyes and substrate for each ordinate with a standard quantity in the same units. The standard quantity is varied by a motor which responds to the differential between the summed ordinate quantities and the fraction of the standard quantity produced by movement of the motor. In the case of voltages the motor operates the movable arm of a potentiometer or rheostat supplied with standard voltage and the voltage between one terminal and the movable arm is connected in opposition to the Voltage corresponding to the sum for the dyes and substrate for the ordinate, preferably or angular using a suitable relay to operate the motor. The motor will obviously turn until the movable arm of the potentiometer is set to the same voltage as that corresponding to the ordinate. Other electrical quantities such as capacities may be compared in a similar manner. In the case of mechanical Weights the motor will vary the amount of the standard weight, for example, the length of a chain. The amount of movement of the balancing motors is used to set up three quantities for each ordinate which are attenuated in accordance with the tristimulus coef"- cient of the wave length corresponding to the ordinate. In the case of voltages three equal voltages may be generated and attenuated by three different potentiometers, or potentiometers may be equally driven across three voltages proportional to the tristimulus coeiicient. In analogous methods other electrical units may be compared. In the case of mechanical weights the Weight may be increased, for example, by lowering a chain from a cam shaped pulley.

In the case o electrical quantities it is pcssible to eliminate motors, as the tristimulus values can be obtained from the output of electronic ampliers ci suitable design with an accuracy suiicient for moet practical purposes. Extreme, and for most purposes unnecessary, accuracy is sacrificed for a more rugged and simpler apparatus with fewer moving parts.

The final result of the above step produces three quantities proportional to the tristimulus values of each ordinate. rIhe tristimulus values of the ordinates are then added to produce three integrated quantities, each corresponding to the sum of the particular tristimulus values of all of the ordinates. This is done in a manner similar to the addition of the quantities produced by the first step, but the addition is across the ordinates instead of the diiIerent dyes and substrate for a single ordinate.

The three integrated tristimulus Values obtained almost instantaneously by the process of the present invention are useful as such. In other words, this sub-combination constitutes a useful process or machine and represents a tremendous advance over what was hitherto possible because the integrated tristimulus values of a mix are determined almost instantaneously. If these are to be compared with integrated tristimulus values oi the dyeing to be matched, the comparison is immediate and the concentrations of the various dyes may be manually varied bit by bit until a match results. The speed depends on how close the original concentrations approach the nal desired result and on the skill of the operator in determining what new concentrations to try. However, as the integrated tristimulus values of a new arrangement oi concentration is given by the process or machine of the present invention practically Vinstantaneously the cut and try method is speeded up by such an enormous factor that it becomes entirely practicable. Matches can be obtained under favorable circumstances manually in from ve to fteen minutes as against hours which were required before. This great increase in speed renders the modiiication of the present invention, which includes only the steps or elements described above, a thoroughly practical process or instrument which represents a great advance over what was hitherto possible. However, even with the substantially instantaneous determination of integrated tristimulus values for any mix the machine still requires skilled operation and automatic and the process vof the blue4 dyes.

` to be matched.

values, butrit will have a greater effect on the judgment .of the skilled operator. It is not does not automati- It merely speeds up cally produce a match.

integrated tremendously the determination of tristimulusvalues of mixes.

l It is desirable to eliminate the skill or the operator and still 'further increase ythe speed of matching, by carrying out automatically the operations which vthe skilled operator has togo .through in setting up `successive trial mixtures,` vand to this further refinement of the process and machine aA preferred embodiment or the present invention is directed. 1t will be 'obvious `that what a skilled operator does when he uses the sub-combination of the present invention described above is to vary the concentration of the different dyes in such a manner as to bring the integrated tristimulus values close and closer tothe true integrated tristimulus values of the dyeing to be matched. En the case of the operator his judgment informs him that certain dyes will have a relatively large aifect on one or other tristimulus value. For instance, the integrated tristimulus value X is aiected very greatly by a'blue or violet, or'even to a lesser extent magenta dye, whereas it is afected much less by a yellow dye. Correspondingly a yellow dye would aiect the integrated tristimulus value Z to a great degree. Therefore, the'skilledoperator, if he viinds that the integrated tristimulus value X too low willdecrease the concentration In other words, if three dyes are used to produce a mixl each of the dyes may I, be chosen so that each aiects most strongly one integrated tristimulus value.

Ther automatic matching then proceeds by ,the same method as is used in obtaining the three quantities for the original integrated tristimulus values, namely, the comparison of the quantity represented by the tristimulus value produced on the machine .or produced by the process with the tristimulus value or the shade IThe differential, through suitable electrical or mechanical relays ii" necessary, can then move the elements which determine v the concentration of the particular dye which has `a large effect on thatintegrated tristimulus value. For example, ii profile templates yare used, this differential maycause a motor to move the template in a ldirection which would correspond to increasedl or decreased concentration.

VAO f ycourse the change in concentration at any time will affectall three integrated tristimulus the one which it more nearly complements. The lastA step will result in a balancing which will automatically change the concentrationsV of the dyesv bringing them closer and closer to a lper- `rect match with the lintegrated tristimulus values of the dyeing. lIn the ycase of the `preferred vmachine oi the present invention the operation is very rapid and may take from a few seconds to a minute. The final result is not only produced at a speed which is almost instantaneous compared to the hours that were required by mathematical calculation, but the process and the apparatus are entirely independent of skilled operation and their accuracy is just as high with lan unskilled operator as With a man who had had great experience in judging color.

` There are two general ways in which integrated tristimulus valuesy may be obtained. rThese are known as the selected ordinate and weighted vordinate methods. In the selected ordinate method ordinates are selected in diiierent parts` .8 of the spectrum for each tristimulus value, and these ordinates are then treated equally. This eliminates the `question of diierent degrees of CFL ` many yordinates for each color because the ordiv'hates for each integrated tristimulus 'value are different.

The weighted ordinate system utilizes a single `set of ordinates f properly chosen through the spectrum, and the product corresponding to each ordinateiis then attenuated electrically or mechanically to produce three different quantities corresponding to4 the relative tristimulus values for the? particular wave length. While this does involve an additional step the enormous simplification which is effected by using only a single set of ordinates for each color will ordinarily render the weighted ordinate method preferable, andy in fact this is' the preferred form of the present invention. The preference has nothing todo with elective operation. Just as good results canbe obtained by the selected ordinate ,method but the latter, except in exceptional circumstances,` involves more complex and more expensive apparatus.

Fig. 1 is an elevation of four template racks; Fig; 2 is a wiring diagram of a portion of the modification shown in Fig. 1';

Figv is va side view of the potentiometer drives of one ofthe template racks of Fig. 1;

` Fig. 4 is a bottom view corresponding to Fig. 3; Fig. `5 is a top View of the potentiometer drives shown in Fig. 3;

K Fig. 6 is a detailed enlarged vertical section through one lof the potentiometers;

Fig. 7 is a sectionthrough a template rack along the line '1 -I of Fig. 1 using condenser-s v instead of potentiometers;

Fig. 8 is alhorizofntal section through Fig. 7 along the line 8 8;

,Fig 9 is a perspective of the two condenser plates of Fig.7;

Fig. 10 isa wiring diagram of a portion or the modification shown in Figs. 7 to 9;

Fig; 11 is an enlarged vertical section through Ythe capacity matching device shown in Fig. 1i);

Fig.: 12 is a wiring' diagram of a modication using tapped resistors instead of templates;

Fig. 16` is a diagrammatic plan view of a modi- `fication employing chainomatic balances;

Fig. l1'7 isa vertical elevation of the modiiication of Fig. 16; and

Fig. 18 is a perspective of representative porjtionsv of the modification shown in Figs. 16 and Y 17, and

Fig. 19 is a block diagram of the apparatus for'three wavelengths and three dyestus.

l Theinvention will be described generally in connection with Fig. 19 which is a block diagram `orthree dyestuffs and three wave-lengths.

, They figure shows nine elements, one for each `dyestuff A, B and C for each wavelength. The

wavelengths will be referred to by numbers, so that the blocks are Vdesignated Al, A2, A3, Bi,

B2, etc. In these elements there are generated groups of equal physical quantities proportional to concentration of the three dyestuffs. The outputs of these elements are designated AIC, A2C, A3C, etc. A second group of elements, designated AIK, A2K, A3K, etc., are responsive to the outputs and produce outputs proportional to concentration multiplied by light additive function K of each dyestuff at each wavelength. The outputs of this second group are therefore designated AI CK, A2CK, A3CK, etc. These last outputs are summed for each wavelength to produce three quantities corresponding to the sum of the CKs for the mixture of dyestus, and are designated MICK, M2CK and MSCK. Three elements, IKR, 2KB and SKR are actuated by the three MCK quantities respectively, and produce output quantities corresponding to the reflectance of the mixture of the dyes for each wavelength, and are designated MIR, MZR and M3R. The quantities are non-linear functions of K and the wavelength corresponding to the relation between K and reflectance:

b is body reectance, s is surface reflectance, and K is the additive light absorption function.

The three KR elements actually generate not one MR quantity but three equal ones, each of which actuates a separate element Xi, Yi, ZI, X2, Y2, Z2, etc. These elements transform the MR quantities into outputs proportional to reflectance times the tristimulus coecient of the particular tristimulus X, Y or Z for the particular wavelength I, 2 or 3. The outputs are designated IRX, IRY and IRZ respectively. The three )E quantities are summed to a quantity IX representing the integrated tristimulus value for X, and in a similar manner, two other sums representing the integrated tristimulus value Y and integrated tristimulus value Z are obtained. Three other predetermined integrated tristimulus values 10X, IoY and IoZ are generated, corresponding to the integrated tristimulus values of a shade to be matched. The two integrated tristimulus values for X are then introduced into a diierential element DX which generates an output proportional to the differential between 10X and IX, which is designated IoX-IX. This quantity actuates the elements AI, A2 and A3. Similarly differential element DY produces a quantity IoY-IY, and a difierential element DZ produces a quantity IZ-IZ; which quantities control the elements BI, B2 and B3, and CI, C2 and C3 respectively.

The choice of the elements AIK, AZK, A3K, etc., that is to say, the choice of dyestuffs, and the phasing of the differential quantities I0X-IX, etc., are so made that the actuation of the elements AI, A2, A3, etc., is in a direction to reduce the differential quantities. The machine operates when the proper choice of dyestuis has been used to reduce the differentials to zero. Indicators, represented by the conventional dial and pointer, show the magnitude of the quantities proportional to concentration applied to the elements AI, A2, A3, etc. In other words, these indicators show the concentrations of the chosen l0 dyestuis necessary to match the predetermined shade.

Fig. 19 has been limited to three dyestuls and three wavelengths in order to provide a clear diagrammatic showing. In practice, of course, there may be more than three dyestuffs, and there will usually be a K element corresponding to substrate. Various modifications of the invention will be described in detail in Figs. 1-18 where a larger number of ordinates, eleven, are illustrated.

The modiiications of the invention using voltage or capacity addition described in Figs. 1 to 14 are shown in connection with color matching involving three colors and a substrate. As most of the elements are duplicated for each color and substrate they will bear the same reference characters, with the subscript A, B or C for the particular dye, or D for the substrate. In a similar manner elements associated with each of the three tristimulus curves of Fig. 15 will bear the subscript X, Y and Z of the corresponding tristimulus.

Figs. 1 to 6 show a modication using Voltage addition and dye and substrate templates. In Fig. 1 there is shown four template guide frames I3, each provided with eleven slots I2, in which the pins I to II can move. The frames accommodate templates A, B and C for the three colors and D for the substrate, the profile of the templates corresponding to the logarithm of the additive function K of the dyes and substrates. Vertical motion of the templates results in positions of the pins IA to IIA, IB to IIB, Ic to IIc, respectively, corresponding to the logarithm of the product of K with dye concentration. The templates carry a reference mark I5 which move along scales I4 on the template frame, the scale being logarithmic and showing concentration of the dye corresponding to the particular position of the template in each frame. Movement of the template is eiected by a rack I'I having a clamp I6 and moving through bearings 20 on each template frame. Each rack meshes with a pinion I8 which is driven through a worm I9 from an electric motor. The motor driving template A bears the character MX, that driving template B, MY, and that driving template C, MZ. These designations indicate that the motors are driven respectively in accordance with voltages determined by the three integrated tristimulus values X, Y and Z of the mixture of the dyes, respectively. The rack for the substrate template D is set by the hand screw 32 and does not move during any particular color match as the concentration of the substrate does not change.

The pins I to I I in each frame are clamped to endless cables 4I to 5 I, respectively. These cables at one end run over a series of idler pulleys II to SI (Fig. 5), and then aroimd the pulleys of corresponding potentiometers 2I to 3| (Figs. 3 to 5). Three of the cables, 43, 4'! and 5I, run straight. The other cables are deilected down by pulleys 33 to 4U (Figs. 3 and 5) in order to permit a staggered mounting of the potentiometers 2l to 3|.

The potentiometers are of a conventional logarithmic type and the drive is illustrated in Fig. 6 for the potentiometer numbered 22. The pulley is shown at 52 and turns a shaft 63 journaled in an arm 8f3 which is clamped to the potentiorneter supporting bracket 33, the latter being in turn fastened to the main framework of the template frame. Rotation oi the pulley S2 is opposed by the coiled spring 64 which tends to ill turn the pulley so that when there is no template in the frame the pin 2 is at the top of its, slot. To the shaft b3 there is clamped an arm 65 bearing at one end a fork t@ with a sharp wheel El running between the coils 22 of the potenti-r ometer. The other end carries a moving contact 68. Wires @s and iii connect to the two ends of the potentiometer resistance. As shown the vpotentiometer maires ive full revolutions to cover the whole of its resistance. The resistance is of conventional coiled wire type and is, of course, non-uniform, as in all logarithmic potentiometers. The scale of Fig. 6 is too small to show this non-linearity. Y

Fig. 2 is a wiring diagram for the pins ZZA-21).` The potentiometers 22A-222D are shown diagrammatically as logarithmic potentiometers across batteries @2A- 921). The voltages between the negative ends of the potentiometers and the sliding contacts @SA- tido are designated VAKZ, VBKE, VCKZ, and VDI/I2, the notation indicating that the voltage is proportional to K times concentration ci the dye A at the wave length corresponding to 2, and so on. y

The four voltages are connected in series and therefore added, the sum being designated VKM, a notation indicating that it is the voltage proportional to the sum of the functions K for the mixture oi dyes and substrate, and for the wave length of the spectrum corresponding to pin 2. rlhis voltage is connected in opposition to a voltage produced by battery d and rheostat Sii having ar sliding Contact connected to the other end of the battery through a resistance 8i small in comparison to S55. The sliding armv 8l is connected to the center tap of a `coil 32 of the input transformer' di oi a vacuum tube amplifier S3. The two ends ofk the coil 32 are connected to contacts t@ and Q5 which can be successively engaged by the vibrator contact @3, which is connected to slider Vibration is eiected in the conventional manner by a magnet 95 and coil 9i connected to the A. C. line ltd. The difference between the voltage from the battery 85 and the voltage VBZZM is thus applied in the form of alternating potential to the ampliiier 93, the voutput of which is led through wires @Si to a balancing motor t8, which drives the moving arm 8l of the rheostat d6 in a direction to reduce the differential. When the arm 8l has been moved to a point at which the voltage from the battery 85- is exactly equal and opposite to VKZM the motor 88 stops. This device is shown in diagrammatic form only, as its structure forms no rpart of the present invention and the unit is a piece of standard electrical equipment which can be purchased on the open market.

The motor 8f3 turns acam 89 which jcarries a follower gli driving the sliding arms lil to lH3 of three equal potentiometers lili to lit, across batteries iii to H9. It will be noted that since the balancing ,voltage generated bythe battery 85 is applied through a rheostat the movement of the cam d@ proportional not to VKZM but substantially to its reciprocal. The profile of the cam dii is so chosen that the voltages produced from the potentiometers llfl to il@ are proportional toy reflectance of the mixture of 4dyesA and substrate at the wave length correspondingto pin 2.Y The transformation from reciprocal of VKRM instead of VKBM itself is chosen because at certain points the change of reflectance, R, with K, is too rapid to permit reliable operation o a'cam and follower. The steepness of the i2 cam transforming l/K into R is suiciently moderate so that a reliable cam actionis possible. The voltages generated by the potentiometers lid to l it are applied across tapped resistorsk l2!) to i222. In order yto produce a voltage which is a constant fraction of the potentiometer voltage within the accuracy of the whole method of the present invention, the resistance of the tapped resistors is very much greater than the resistance of the potentiometers. For example, they may be one thousand times-as great. The resistors are tapped to give a proportion of the total voltage corresponding to the tristimulus coefficients for each of the three stimuli at the wave length corresponding to the pin number, as is shown in Fig. l5. proportion to each tristimulus coeflicient for the reflection of the mixture of dyes andsubstrate,

they are designated VPUEMX, VREMY, and

VREMZ, respectively.

The voltages for each tristimulus are connected in series, asis shown for tristimulus X in Fig. 2. The sum oi the voltages corresponding to tristimulus X is connected in opposition to the voltage from a battery and potentiometer lill. This potentiometer isset manually in accordance with the integrated tristiniulus value X of the color shade to be matched. rIhe slider of potentiometer tdi is connected to the center tap of coil it of the input transformer iliii of avaeuum tube amplifier il@ of the same design as amplifier 93. In a similar manner the diiierential between the sum or the tristimnlus voltages X and the Voltage from the potentiometer lill is applied onto a vibrator arm ist which is vibrated by the A. C. coil itil and magnet it@ to alternately'strike contacts i liti and iii, which are respectivelyconnected to the ends or" the coil Hi8. The differential of the voltage is therefore applied to the amplifier ils in therorm oran alternating voltage in precisely the same manner as the diilerential voltage was applied to the amplier 93.

The output of the amplifier l iii drives the n10- torMX (Fig. l), which moves the template for dye A. The motor turns in a direction to decrease the dilerential input to the amplifier H0; In a similar ymanner the voltages VRIMY- VRi iMY, and VltiMZ-Vlti ilViZ are matched with potentiometers set to the tristim-ulus values Y and Z and drive motors MY and MZy through ampliers, the circuits of which are the same as amplifier i iii. lis these circuits duplicate the one shown in Fig. 2, they are not illustratedv in the drawings.

In the operation of the modification just described in connection with Figs. l to 6 dyes A, B and. C are chosen of Ysuitable general colors, and the integrated tristimulus values X, Y and Z of the mixture of dyes and substrates are opposed by the three voltages set'on potentiometer itil and the other two correspondingpotentiometers (not shown) in accordancewith the integrated tristimuius Values of the shade to be matched. Amplifiedv diiierential `voltages turn the motors MX, MY and MZ in directions to decrease these differentials, and iinally the motors come to rest at positions or templates A, B andC, which will produce a perfect match or the shade desired. The concentration of the dyes A, B and C is read by the pointers iEA to ic on the scales MA to l fic, respectively.

Figs. 7 to li illustrate a modiiication in which condensers are used in place of potentiometers or other Voltage generators. The pins ofthe template frames instead of being clamped to Since these voltages are in.

cables are fastened to movableplates' |29 (Figs. 7 and 9) which are providedwitha second supporting button |27, and which are moved 'by the templates against the tension of springs such as |28. The movable condenser plates |29 are provided With fixed condenser plates |30 of a shape such that the capacity variesin accordance with the additive function K as theplate |29 moves in accordance with log K.

Fig. 8 shows four pins, to 4, attached to movable plates |3| to |34, which cooperate with iiXed plates |35 to |38. The movableplates are provided at the top with flanges |23 to |26 which keep the plates accurately in alignment. As far as the frames and templates go the operation proceeds precisely as described in conjunction with Figs. 1 to 6 where voltages were generated.

Fig. shows a capacity Wiringdiagram for the pin 2 analogousto Fig. 2. The movable plates |32A|32D are connected in parallel as are the corresponding stationary plates BSA-|3613. The capacities, in accordance with the notation' used for voltages, are designated CaAKZ, CdBK, CaCl/i2, and CaDKZ. rihese four 'capacities in parallel add up to the capacity' CaKZM, and this capacity is impressed across one arm of aWheatstone bridge circuit, which is provided with a conventional source of alternating potential i3d, resistance arms |46 and |4|, and a variable condenser arm |42. The junction point of the resistance arms of the bridge is connected to one end of the input coil |43 of the input-transformer |44 of an amplier |45, and the junction point of the two capacitative arms is connected to the other end of the same coil. An alternating current input signal is, therefore, impressed on the amplier, which is proportional to the ratio between CaKZll/I and capacity of the variable condenser |42. The output of the ampliiier feeds a balancing motor |46, which in turn drives the variable condenser |42. The shape of the plates of this condenser may be so chosen that the rotation of the motor '|45 is proportionaleither to K or to a reciprocal thereof, and lof course the capacity of the condenser is changed in a direction to match CaKZM. At match the bridge is balanced and the motol` |46stops.

The same motor |46 drives three variable condensers |49, |58 and |5|, the plate shape and spacing of which is such that the capacities are proportional to reiiectance of the mixture of dyes and substrates times the tristimulus coefcient for the wave length of the spectrum corresponding to the pin. In accordance with the notation chosen for voltages these capacities are designated as CaRMX, CaRZMY, and CaRZMZ, respectively. rEhe capacities corresponding to the coeiiicient for tristimulus'X for the various Vpins are shown added in parallelin'the same figure.

The sum of the capacities for tristimulus X forms one arm of a second Wheatstone-bridge provided with a source of ralternating potential |59, tWo resistancearms |60 and I6| and amanually adjustable variable condenser |62. The latter is adjusted to a capacity corresponding to the integrated tristimulus value X of the shade to be matched, the procedure beinganalogous to the setting of the potentiometer IUI in Fig. 2. The junction points of the resistance arms and the capacitative arms of the bridge are connected to the two ends of a coil |63 of the input transformer |56 of amplier |65. The circuit operates precisely as does the amplifier |45 but is based on an input signal `which is the ratioibetween the sum of the X tristimulus capacities and the capacity of theY condenser |62. The output' of the ampliiier |t`5 drives motor MX, just as the output or" the ampliiier H!! drove the same motor in the modification using additive voltages.

Fig. 11 shows in a schematic form the condensers |42, H39, |55 and |5| appearing in the Wiring diagram of Fig. 10. The motor |46 is shown as driving a toothed bar 01 rack |53. This bar carries a movable plate |41 of the condenser |42 which cooperates with the Xed plate |48. The same bar moves three movable plates |52, |53 and |54, which cooperate with xed plates |55, |56 and |51, to form the three condensers |49, |5e and |5|. The xed plates |55 to |57 are shown as being the same shape and possessing the proile which will transform the chosen function of El into The relative proportion of the capacity corresponding to each tristimulus coefcient for the wave length of pin 2 is determined by the relative spacing oi the plates in condensers |49, I5@ and |51.

1f desired, the whole of the transformation from K to R need not take place in a single condenser plate. A fixed plate |48 of non-uniform shape may be used. Fig. l1 is purely schematic and representative of the method. In practice, of course, it is undesirable to use condensers with se few plates, as errors due to edge effects would be too high and, therefore, multiplate condensers will normally be used. For simplicity, however, Fig. 11 is shown in a purely schematic form with two plate condensers.

instead of employing template frames and templates, the pronle of which is proportional to the log of K, it is desirable in many cases to employ a system in which a set of eleven tapped resistors are provided for each dye, the tap being so placed as to correspond to K for the particular point of the spectrum corresponding to positions l to 11 in Fig. l5. A set of tapped resistors for three dyes, A, B and C and a substitute D, are shown in Fig. 12, the tapped resistors being designated by the numbers l1 I'to |8| corresponding to points to in Fig. 15, or pins l to in the preceding modifications. The tapped resistors are across secondaries of a series of identical transformers |53 to 368, the primaries of which are connected in parallel and plug into attenuators |51, |88, |69 and |113. The first three attenuators are driven by motors 255, 25D and 255 and the attenuator |10 may be adjusted manually for a particular substrate. All of the attenuators receive voltage from a source of alternating voltage |65. The attenuators which are of conventional design and provided with the usual dials (not shown) have output impedances which are very low compared to the resistance of any of the tapped resistors to lili. For example, the attenuators may have output impedances from about l/iooo to l/iamm of the resistance of a tapped resistor.

The setting of the attenuator multiplied by the factor determined by the tap on 'each resistor results in the production of voltages which are proportional to K times concentration for each of the eleven ordinates for each dye and substrate i. e., C. K. In accordance with the voltage notation used before, these voltages are designated as VAKi to VAKH; VBKl to VBKH; VCKI to l/'CKI i; and VDKI to VDKI The voltages for a particular ordinate or pin position are connected in series. For clarity in Fig. 12 the Wires are not drawn out in full.

Fig. 13 shows an amplier for the ordinate corresponding to position No. 2 which transforms 

